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Topic: Characteristic class

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	Station Information - Characteristic class
		Chararcteristic classes are in an essential way phenomena of cohomology theory - they are contravariant constructions, in the way that a section is a kind of function on a space, and to lead to a contradiction from the existence of a section we do need that variance.
		When the theory was put on an organised basis around 1950 (with the definitions reduced to homotopy theory) it became clear that the most fundamental characteristic classes known at that time (the Stiefel-Whitney class, the Chern class, and the Pontryagin classes) were reflections of the classical linear groups and their maximal torus structure.
		Characteristic classes were later found for foliations of manifolds; they have (in a modified sense, for foliations with some allowed singularities) a classifying space theory in homotopy theory.
	www.stationinformation.com /encyclopedia/c/ch/characteristic_class.html (427 words)

	Characteristic class
		In mathematics, the idea of characteristic class is one of the unifying geometry concepts in algebraic topology, differential geometry and algebraic geometry.
		The characteristic class approachj to curvature invariants was a particular reason to make a theory, to prove a general Gauss-Bonnet theorem.
		What is more, the Chern class itself was not so new, having been reflected in the Schubert calculus on Grassmanians, and the work of the Italian school of algebraic geometry.
	www.ukpedia.com /c/characteristic-class.html (438 words)

	Characteristic class
		In mathematics, the idea of characteristic class is one of the unifying geometric concepts in algebraic topology, differential geometry and algebraic geometry.
		A characteristic class of principal G-bundles is a natural transformation
		Characteristic classes are in an essential way phenomena of cohomology theory - they are contravariant constructions, in the way that a section is a kind of function on a space, and to lead to a contradiction from the existence of a section we do need that variance.
	pedia.newsfilter.co.uk /wikipedia/c/ch/characteristic_class.html (515 words)

	The Postmodernism Generator: Communications From Elsewhere
		"Class is part of the fatal flaw of sexuality," says Derrida; however, according to Brophy[1], it is not so much class that is part of the fatal flaw of sexuality, but rather the defining characteristic of class.
		However, the characteristic theme of Scuglia's[6] essay on neocultural sublimation is the role of the poet as writer.
		In a sense, the characteristic theme of von Junz's[19] analysis of cultural feminism is not, in fact, theory, but subtheory.
	www.elsewhere.org /cgi-bin/postmodern/899929013 (2097 words)

	Dror Bar-Natan:Classes:2001-02:Algebraic Topology
		Class notes for March 12th (the basic idea of algebraic topology, Brouwer's theorem, the fundamental group, the fundamental group of the circle).
		Class notes for May 7th (the intuition of homology, precise definition, the square of the boundary map, the homology of a point).
		Class notes for June 20th (the homology of the comlement of a sphere in another one, applications to the linking number, invariance of domain).
	www.math.toronto.edu /~drorbn/classes/0102/AlgTop (510 words)

	Stiefel-Whitney class - Wikipedia, the free encyclopedia
		Stiefel-Whitney classes arise in mathematics as a type of characteristic class associated to real vector bundles
		The first Stiefel-Whitney class is zero if and only if the bundle is orientable.
		The second Stiefel-Whitney class is zero if and only if the bundle admits a spin structure.
	en.wikipedia.org /wiki/Stiefel-Whitney_class (162 words)

	Activation Example
		Characteristics and characteristic values of the material are displayed; these are for r-4000 in IDES: Color coat number 3 and color red.
		You are now familiar with the information which you need to enter the correct formula in the activation column of the process template; namely, material class, characteristic and characteristic value.
		The activation requirement represents: activation of the business process when the material characteristic value of the PC (the entered material number) is not equal to the standard color (that is, white, red, green or blue).
	help.sap.com /saphelp_45b/helpdata/en/37/ac9fefd45411d1a5b10000e82de878/content.htm (544 words)

	Forensic paper on unusual rifling marks on bullet pieces
		The jacket pieces with additional rubbing and impact marks, may not be identifiable even to the extent of elimination on the basis of class characteristics although initially they bore characteristic rifling marks.
		The engravings in most of these were sufficient for the identification of class characteristics (direction of rifling, angle of rifling, width of rifling, etc.) Fig.1(a)and fig1(b).
		As such, the characteristic marks on the lead core can be examined and compared with the rifling marks on the test bullets by usual procedure.
	www.geocities.com /j_ksinha/urifling.html (672 words)

	[No title]
		Mapping Class Groups, Characteristic Classes and Bernoulli Numbers GUIDO MISLIN ETH Z"urich, Switzerland; and Ohio-State University, Columbus, Ohio Introduction The mapping class group g of a closed, connected and oriented surface Sg of genus g is defined as the group of connected components of the group of orienta* *tion preserving diffeomorphisms of Sg.
		The characteristic classes are related to the denominator* s of Bernoulli numbers, the Euler characteristic* involves the whole Bernoulli number* s, and our theorems concerning the Yagita invariant have to do with the notion of regular primes, which is expressible in terms of numerators of Bernoulli number *s.
		In Section 6 this Euler class is related to the Euler characteristic O(g) of the group g, an* *d in Section 7 we discuss periodicity phenomena of g as well as the Yagita invariant.
	hopf.math.purdue.edu /Mislin/bernoulli.txt (11294 words)

	Zvon - RFC 892 [ISO Transport Protocol Specification] - PROTOCOL CLASSES
		Class 1 has been designed to be used in association with type B network connections.
		For Class 2 the explicit variant of the 'release' mechanism is used, enabling transport connections to be cleared independently of the underlying network connection.
		Class 4 has been designed to be usd in association with network connections of type C. 7.4.2 Functions of Class 4 This class provides the functionality of Class 3, plus the ability to detect and recover from lost, duplicated or out of sequence TPDUs without involving the user of the transport service.
	www.zvon.org /tmRFC/RFC892/Output/chapter7.html (6918 words)

	IMF: IMF Event Calendar
		The general version of the RR theorem for D-modules due to Schapira and Schneiders expresses the Euler characteristic of an elliptic D-module by the integral of its characteristic class, the so called microeuler class.
		Identification of microeuler class with the Connes-Karoubi chern class in negative cyclic homology 2.
		Structure theory of the deformation of the sheaf of holomorphic functions on the cotangent bundle of a complex manifold associated to microdifferential operators 3.
	www.imf.au.dk /cgi-bin/dlf/viewevents.cgi?id=997&dlang=en (116 words)

	Sinha's forensic firearm paper on bullet identification
		Characteristic class marks on jacketed bullets can not be compared with the marks on unjacketed bullets fired through such barrels.
		The characteristic break, shape, size, relative position of rifling marks and shaving can be used to identify the fired bullet in respect of the firearm.
		The importance of these characteristic marks is clear, especially when the bullets are mutilated and characteristic striations of land and groove marks are not sufficient to permit identification.
	www.geocities.com /j_ksinha/nsrifling.html (695 words)

	Chern-Simons form - Wikipedia, the free encyclopedia
		In mathematics, the Chern-Simons forms (pronounced chen simons) are certain secondary characteristic classes.
		They have been found to be of interest in gauge theory, and they (especially the 3-form) define the action of Chern-Simons theory.
		The theory is named for Shiing-Shen Chern and James Harris Simons, co-authors of a 1974 paper entitled "Characteristic Forms and Geometric Invariants," from which the theory arose.
	www.wikipedia.org /wiki/Chern-Simons (182 words)

	[No title]
		The CharacteristicHome, which was designed and implemented along with the Characteristic class, has the method to retrieve all the instances of Characteristic that belong to a particular BaseObject.
		Characteristics should be thought of as providing the interface to measurements, attributes, and other information about some object.
		Characteristic Group Characteristic Groups are a collection of references to Characteristics or Measurements that can be an independent named object or that may belong to some other object.
	www.omg.org /docs/mfg/00-08-05.txt (9489 words)

	DESCRIPTION OF CLASS 4: ERROR DETECTION AND RECOVERY CLASS (Site not responding. Last check: 2007-10-21)
		The characteristic of Class 4, in addition to those of Class 3, is the detection of errors which occur as a result of the low grade of service available from the network layer.
		This detection of errors is made by extended use of the sequence numbering of Classes 2 and 3, by a timeout mechanism, and by additional protocol mechanisms.
		Class 4 does not attempt to deal with detection of errors due to the misdelivery of TPDU s.
	ganges.cs.tcd.ie /undergrad/4ba2/transport/5.a.37.html (202 words)

	Diamond.info - Diamond and engagement ring guide
		The class 2 characteristic should be within 2% or 2 degrees of the 1B characteristic.
		Only a single 3A characteristic is permitted and the 3A characteristic cannot be a very thick girdle or more than 1 degree too shallow a crown angle.
		Stones with class 4 extremely thick or extremely thin "overall" girdles are not graded as class 3.
	www.diamond.info /diamonds/diamonds_4cs_cut5.shtml (613 words)

	State-Wide-Policies for MN > Water Quality Standards -- U.S. EPA
		The quality of Class 3A waters of the state shall be such as to permit their use without chemical treatment, except softening for groundwater, for most industrial purposes, except food processing and related uses, for which a high quality of water is required.
		The quality of Class 3B waters of the state shall be such as to permit their use for general industrial purposes, except for food processing, with only a moderate degree of treatment.
		The quality of Class 3C waters of the state shall be such as to permit their use for industrial cooling and materials transport without a high degree of treatment being necessary to avoid severe fouling, corrosion, scaling, or other unsatisfactory conditions.
	www.epa.gov /ostwater/standards/wqslibrary/mn/mn_5_0223.html (487 words)

	ISO/IEC JTC1/SC34 N268
		For each topic or association the class it belongs to is found, and the characteristics of the topic or association are then validated against the constraints in the class.
		Each characteristic is compared with the constraints until a constraint matching the characteristic is found; the characteristic is then validated against that constraint.
		What this class definition does is to say that associations of this type must contain one role of type 'product', the player of which role must be of the same type, and one role of type 'standard', and that the player of this role must also be of type 'standard'.
	www.y12.doe.gov /sgml/sc34/document/0268.htm (1459 words)

	Minnesota Rule 7050.0224
		The quality of Class 4A waters of the state shall be such as to permit their use for irrigation without significant damage or adverse effects upon any crops or vegetation usually grown in the waters or area, including truck garden crops.
		The quality of Class 4B waters of the state shall be such as to permit their use by livestock and wildlife without inhibition or injurious effects.
		The quality of Class 4C wetlands shall be such as to permit their use for irrigation and by wildlife and livestock without inhibition or injurious effects and be suitable for erosion control, groundwater recharge, low flow augmentation, stormwater retention, and stream sedimentation.
	www.revisor.leg.state.mn.us /arule/7050/0224.html (497 words)

	General Conclusions (Site not responding. Last check: 2007-10-21)
		If the comparison for non-equivalent classes is the confound for the individual course comparisons in Study 3, then the overall comparison should be considered as a better indication of Class Characteristic Components.
		These Class Characteristic Components are supposed to tap into the intrinsic and extrinsic motivators of the students.
		A practical implication of this research is that designing courses to incorporate the Class Characteristic Components may offer students important training that will facilitate their successful transition from college to the workforce.
	lilt.ilstu.edu /saskers/thesis/general_conclusions.htm (1813 words)

	SR View a Class (Schedule of Classes) (Site not responding. Last check: 2007-10-21)
		Additionally, if there are two sets of one lecture/two discussions, the lectures should be sections 0001 and 0002 respectively; the discussions should be 0101/0102 and 0201/0202 indicating that the discussions beginning with 01 are correlated to the lecture section 0001 and discussions beginning with 02 are correlated to lecture 0002.
		Note: Each single component class section should have a unique Associated Class number which is the same as the number used for that class’s section ID. Associated Class numbers are used to group simple co-requisites, though, so a lecture/lab/discussion combination that is required to be taken together should all share an Associated Class number.
		Note: General characteristic of class for reporting purposes and for printing in Schedule of Classes.
	www.iupui.edu /~seshelp/training/SR_View_a_Class_(Schedule_of_Classes).htm (765 words)

	BOOK OF FUNDAMENTALS: COMPONENTIAL MANIFESTATIONS [OF EXCLUSIVISM] _______________
		Now, an exclusivism is aggrandizemental if a high(er) value is assigned to a certain class or characteristic quality, and abnegational if a low(er) value is assigned to that class or quality.
		The norm of inclusivity prescribes the inclusion of other classes than the ones to which one belongs oneself, and of other persons on equal terms with one's own class, characteristics and person, and vice versa.
		By complement is, then, to be understood the set of all classes or characteristics other than the one excluded or made exclusive, but belonging to the same field.
	www.trinp.org /MNI/BoF/2/1/4.HTM (1164 words)

	Java Programmer's SourceBook : Thinking in Java (Site not responding. Last check: 2007-10-21)
		A constructor for the base class is always called in the constructor for a derived class, chaining upward so that a constructor for every base class is called.
		This step is repeated recursively such that the root of the hierarchy is constructed first, followed by the next-derived class, etc., until the most-derived class is reached.
		This means that you must be able to assume that all the members of the base class are valid when you’re in the derived class.
	codeguru.earthweb.com /java/tij/tij0082.shtml (1577 words)

	The Ultimate Pontryagin class - American History Information Guide and Reference (Site not responding. Last check: 2007-10-21)
		In mathematics, the Pontryagin classes are certain characteristic classes.
		Pontryagin classes have a meaning in real differential geometry — unlike the Chern class, which assumes a complex vector bundle at the outset.
		The Pontryagin classes of a smooth manifold are defined to be the Pontryagin classes of its tangent bundle.
	www.historymania.com /american_history/Pontryagin_class (329 words)

	How to calculate the characteristic class of an E8 bundle (Site not responding. Last check: 2007-10-21)
		I know that to calculate the pontrjagin class of a bundle with structure group G=O(k) we consider Det(tI - F/(2\pi)), where F is the mxm matrix valued curvature form, and the coefficient of t^{m-2} gives p_1(M).
		Similarly for the Chern class (G=U(k)) we consider Det(tI + iF/(2\pi)) and the first class is given by the coefficient of t^{m-1}.
		For example in Witten's paper "On flux quantization in M-theory and the effective action" he says the topology of E8 means the only restriction on the class of the E8 bundle is that it's integral.
	www.lns.cornell.edu /spr/2003-04/msg0050436.html (189 words)

	Example 2 (Site not responding. Last check: 2007-10-21)
		However, you can also define a value set for class CL2 that is different to the value set for class CL1, by overwriting the characteristic for class CL2, for example.
		When you allocate class CL2 to class CL1, you restrict the allowed value set for characteristic C1 to 10-20.
		The system calculates the subset of the allowed values for the characteristic in class CL2 and the values you entered when you classified the class, so the value set is now 15-20.
	help.sap.com /saphelp_40b/helpdata/es/24/47664d416711d189ec0000e81ddfac/content.htm (142 words)

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